Problem: Simplify the following expression: $t = \dfrac{-4x^2 + 44x - 72}{x - 2} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-4$ , so we can rewrite the expression: $ t =\dfrac{-4(x^2 - 11x + 18)}{x - 2} $ Then we factor the remaining polynomial: $x^2 {-11}x + {18} $ ${-2} {-9} = {-11}$ ${-2} \times {-9} = {18}$ $ (x {-2}) (x {-9}) $ This gives us a factored expression: $\dfrac{-4(x {-2}) (x {-9})}{x - 2}$ We can divide the numerator and denominator by $(x + 2)$ on condition that $x \neq 2$ Therefore $t = -4(x - 9); x \neq 2$